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11.
Kochocki JA Allison WW Alner GJ Ambats I Ayres DS Balka LJ Barr GD Barrett WL Benjamin D Border P Brooks CB Cobb JH Cockerill DJ Coover K Courant H Dahlin B DasGupta U Dawson JW Edwards VW Fields TH Kirby-Gallagher LM Garcia-Garcia C Giles RH Goodman MC Heller K Heppelman S Hill N Hoftiezer JH Jankowski DJ Johns K Joyce T Kafka T Litchfield PJ Lopez FV Lowe M Mann WA Marshak ML May EN McMaster L Milburn RH Miller W Napier A Oliver WP Pearce GF Perkins DH Peterson EA Price LE Roback D Rosen DB 《Physical review D: Particles and fields》1990,42(9):2967-2973
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Bruce J. West Raoul Kopelman Katja Lindenberg 《Journal of statistical physics》1989,54(5-6):1429-1439
The conditions for macroscopic segregation ofA andB in a steady-stateA+B 0 reaction are studied in infinite systems. Segregation occurs in one and two dimensions and is marginal ford=3. We note the dependence of these results on the precise experimental conditions assumed in the theory. We also note the difference between these results and our earlier ones for finite systems where the critical dimension isd=2. 相似文献
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For an arbitrary poset P, subposets {P
i
: 1ik} form a transitive basis of P if P is the transitive closure of their union. Let u be the minimum size of a covering of P by chains within posets of the basis, s the maximum size of a family of elements with no pair comparable in any basis poset, and a the maximum size of an antichain in P. Define a dense covering to be a collection D of chains within basis posets such that each element belongs to a chain in D within each basis poset and is the top of at least k-1 chains and the bottom of at least k-1 chains in D. Dense coverings generalize ordinary chain coverings of poset. Let d=min {|D|–(k–1)|P|}. For an arbitrary poset and transitive basis, a convenient network model for dense coverings yields the following: Theorem 1: da, with equality iff P has a minimum chain decomposition in which every pair of consecutive elements on each chain are comparable in some basis poset. Theorem 2: usda. Theorem 3: s=d iff s=a. The most interesting special case is where the transitive basis expresses P as the product of two posets, in which case u and s measure the minimum and maximum sizes of unichain coverings and semiantichains. 相似文献
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Cerium(III) ions in dilute sulphuric acid medium exhibit a characteristic fluorescence which has its excitation maximum at 260 nm and its fluorescence emission maximum at 350 nm. By utilising the osmium-catalysed redox reaction between cerium(IV) and arsenic(III), microgram amounts of arsenic (7.5–37.5 μg) may be determined by spectrofluorimetric measurement of the ceriurm(III) produced. The principle may be applied to the determination of several other ions which cannot yet be determined by direct spectrofluorimetry, e.g.. Fe(II) (5.6–28 μg), oxalate (8.8–44μg). Osmium(VIII) (0.05–0.2 μg) and iodide (0.6–2.5 μg) may be determined by their catalytic action. 相似文献
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A regressive function (also called a regression or contractive mapping) on a partial order P is a function mapping P to itself such that (x)x. A monotone k-chain for is a k-chain on which is order-preserving; i.e., a chain x
1<...ksuch that (x
1)...(xk). Let P
nbe the poset of integer intervals {i, i+1, ..., m} contained in {1, 2, ..., n}, ordered by inclusion. Let f(k) be the least value of n such that every regression on P
nhas a monotone k+1-chain, let t(x,j) be defined by t(x, 0)=1 and t(x,j)=x
t(x,j–1). Then f(k) exists for all k (originally proved by D. White), and t(2,k) < f(K) <t( + k, k) , where k 0 as k. Alternatively, the largest k such that every regression on P
nis guaranteed to have a monotone k-chain lies between lg*(n) and lg*(n)–2, inclusive, where lg*(n) is the number of appliations of logarithm base 2 required to reduce n to a negative number. Analogous results hold for choice functions, which are regressions in which every element is mapped to a minimal element. 相似文献